DOIAbstract
AbstractWe construct clustered spots for the following FitzHugh–Nagumo system:ε2Δu+f(u)-δv=0inΩ,Δv+u=0inΩ,u=v=0on∂Ω,where Ω is a smooth and bounded domain in R2. More precisely, we show that for any given integer K, there exists an εK>0 such that for 0<ε<εK,εm′⩽δ⩽εm for some positive numbers m′,m, there exists a solution (uε,vε) to the FitzHugh–Nagumo system with the property that uε has K spikes Q1ε,…,QKε and the following holds:(i)The center of the cluster 1K∑i=1KQiε approaches a hotspot point Q0∈Ω.(ii)Set lε=mini≠j|Qiε-Qjε|=1alog1δε2ε(1+o(1)). Then (1lεQ1ε,…,1lεQKε) approaches an optimal configuration of the following problem:(*)Given K points Q1,…,QK∈R2 with minimum distance 1, find out the optimal configuration that minimizes the funct...
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